- Lay, Lay, McDonald, Linear Algebra and its Applications, 5th Ed.
Supplementary Texts (recommended, and in order of increasing difficulty/abstraction)
Supplementary Texts (recommended, and in order of increasing difficulty/abstraction)
Grading: Your grade will be computed as follows:
The midterm will be take place during scheduled class time on Friday, July 24. The final exam will take place during scheduled class time on Friday, August 7, 2020. Homework will be collected on the due dates in our schedule: you will submit them on Canvas. Quizzes will be administered during class time on the scheduled quiz days, and will be submitted on Canvas.
No makeup exams and no makeup quizzes will be allowed, without proper documentation. Let's make this class run smoothly, because there is a lot to cover and timeliness is of the essence! The official policy is the following: If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify your instructor at least two classes in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented illness), that midterm exam score will be replaced by an estimated score based on your performance on the other midterm. If you miss both exams for acceptable reasons, your midterm scores will be replaced by estimated scores based on your performance on the final. If you miss the final exam and have not rescheduled it in advance, you will score zero on the final or receive an incomplete in the course, depending on the circumstances. You may not reschedule a final exam after the exam has started. In order to be excused from an exam for medical reasons, you must either produce a note from a doctor, or you must obtain prior permission from the instructor to miss the exam. Self diagnosis and self medication are not acceptable for this purpose.
Homework: Let us look at these homework problems as the foundation of this course, and let us say that for the most part quizzes and exams will pull from this pool of homework problems or very similar ones. The ideal for us is to work as many problems as possible, for with each worked problem we advance a mile into the conceptual territory we should wish to map out.
Homework problems need to be submitted on Canvas in pdf form! I want a pdf, even if that means taking a picture and converting it to pdf. It is important for grading purposes, because I want to make comments and remarks on pdfs, which I can return to you easily. From my experience last spring, I think the best solution is to use a scanning app on your phone, rather than convert a jpeg. Scanning apps automatically generate a pdf and the way it generates it is much better for printing purposes: much smaller size, simple black-and-white coloring, doesn't eat up toner and take 5 minutes for the printer to spool. Please use a scanning app (or equivalent) to scan all submitted assigments.
You are allowed to use the internet and other resources (e.g. the recommended supplementary books). However! First of all, you must cite your sources when you use them. If you outright copy a solution or a proof, you are required to confess to the fact, and it will cost you a point (it remains to be determined exactly how I'll score the homeworks, but suffice it to say I'll give you roughly a 20% discount). I encourage you all to work together on homeworks, maybe even divide up the problems into smaller groups and then get together to share solutions. We'll discuss strategies in class.
No late homework will be accepted, to help develop regularity of habits, as well as to make everybody's lives more bearable--we are on a tight schedule of five weeks! I will drop your lowest homework score to counterbalance, and will also do the same with quizzes.
Students With Disabilities: If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner (at least one week before the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website www.colorado.edu/disabilityservices/students. Contact Disability Services at 303-492-8671 or email@example.com for further assistance. If you have a temporary medical condition or injury, see Temporary Medical Conditions under the Students tab on the Disability Services website and discuss your needs with your professor.
Student Classroom and Course-Related Behavior: Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. For more information, see the policies on classroom behavior and the Student Code of Conduct.
Statement on Discrimination and Harassment: The University of Colorado Boulder (CU Boulder) is committed to fostering a positive and welcoming learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct intimate partner abuse (including dating or domestic violence), stalking, protected-class discrimination or harassment by members of our community. Individuals who believe they have been subject to misconduct or retaliatory actions for reporting a concern should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127 or firstname.lastname@example.org. Information about the OIEC, university policies, anonymous reporting, and the campus resources can be found on the OIEC website.
Honor Code: All students enrolled in a University of Colorado Boulder course are responsible for knowing and adhering to the academic integrity policy. Violations of the policy may include: plagiarism, cheating, fabrication, lying, bribery, threat, unauthorized access to academic materials, clicker fraud, submitting the same or similar work in more than one course without permission from all course instructors involved, and aiding academic dishonesty. Incidents of academic misconduct may be reported to the Honor Code Council (email@example.com; 303-735-2273). Students who are found responsible for violating the academic integrity policy will be subject to nonacademic sanctions from the Honor Code Council as well as academic sanctions from the faculty member. Additional information regarding the academic integrity policy can be found at the Honor Code Office website.
Pascal, in the opening lines of his Of the Geometrical Spirit (c 1657) says, `We may have three principal objects in the study of truth: one to discover it when it is sought; another to demonstrate when it is possessed; and a third, to discriminate it from the false when it is examined. I do not speak of the first [this is speculation, or insight, and involves ingenuity and creativity--these are not uniformly distributed among people and so do not constitute a method]; I treat particularly of the second, and it includes the third. For if we know the method of proving the truth, we shall have, at the same time, that of discriminating it, since, in examining whether the proof that is given of it is in conformity with the rules that are understood, we shall know whether it is exactly demonstrated.`
He then proceeds to explain the method of proof. Step one is establishing clear definitions, step two is proofs, `never advancing any proposition which could not be demonstrated by truths already known,` whether those be previously proven propositions, our established definitions or the assumed axioms of the subject.
Pascal elaborates more fully on the proper methods of proof in another essay, The Art of Persuasion: 'This art, which I call the art of persuading, and which, properly speaking, is simply the process of perfect methodical proofs, consists of three essential parts: of defining the terms of which we should avail ourselves by clear definitions; of proposing principles or evident axioms to prove the thing in question; and of always mentally substituting in the demonstrations the definition in the place of the thing defined.'
'The reason of this method is evident,' says Pascal, 'since it would be useless to propose what it is sought to prove, and to undertake the demonstration of it, if all the terms which are not intelligible had not first been clearly defined; and since it is necessary in the same manner that the demonstration should be preceded by the demand for the evident principles that are necessary to it, for if we do not secure the foundation we cannot secure the edifice; and since, in fine, it is necessary in demonstrating mentally, to substitute the definitions in the place of the things defined, as otherwise there might be an abuse of the different meanings that are encountered in the terms. It is easy to see that, by observing this method, we are sure of convincing, since the terms all being understood, and perfectly exempt from ambiguity by the definitions, and the principles being granted, if in the demonstration we always mentally substitute the definitions for the things defined, the invincible force of the conclusions cannot fail of having its whole effect.'
Significant portions of these two essays are devoted to discussing key nuances of the method, which require skill, even art, to master:
Two special topics round out his discussion, both in Of the Geometrical Spirit.
The stage has been set for the development of calculus, whose full logical articulation is analysis. Our subject, linear algebra, which is the study of n-dimensional Euclidean space, should be understood as the n-dimensional analog of the tangent line to a curve: the tangent space to an n-dimensional hypersurface in n+1 dimensions, say. What a line is to a curve, an n-dimensional vector space is to an n-dimensional hypersurface, the local linearization (hence the importance of the word linear in linear algebra). This analytic aspect is only touched in Calc 3, but is fully developed in Undergraduate Analysis II. We study its algebraic aspects alone in this class.
All of the above concerns the logical structure of linear algebra. But there is the computational side to consider as well. In this course, we will compute many examples, or, in other words, we will apply the theory to special numerical cases. For this reason, we will avail ourselves also of software and coding. All this will be spelled out in due time, but suffice it to say that the whole design of the theory is guided by numerical considerations from the beginning. It's logic guarantees it's reliability and serves to map out its architecture, while it's purpose is to facilitate computations in practical applications. Both work in harmony towards the same goal.
|Week \\ Day||M||Tu||W||Th||F|
- 7/6 -
- 7/7 -
- 7/8 -
- 7/9 -
- 7/10 -
- 7/13 -
- 7/14 -
- 7/15 -
- 7/16 -
- 7/17 -
- 7/20 -
- 7/21 -
- 7/22 -
- 7/23 -
- 7/27 -
- 7/28 -
- 7/29 -
- 7/30 -
- 7/31 -
- 8/3 -
- 8/4 -
- 8/5 -
- 8/6 -
Homework 1 (due Fri 7/10):
Homework 2 (due Thurs 7/16):
Homework 3 (due Wed 7/22):
Homework 4 (due Thurs 7/30):
Homework 5 (due Thurs 8/6):